Microlenses are used to funnel light of a larger area into a photodiode of an imager pixel, for example. Microlenses also can be used to trap light into a solar cell, as well as to project light from a light-producing component of a display. Advanced products and systems that utilize microlenses in these and other similar ways include, without limitation, digital cameras, flat-panel visual displays, and solar panels. Such products and systems are used in a wide variety of applications ranging from mobile phone displays and flat-screen televisions to mapping the solar system, and beyond.
The direction that light is propagated through two media, such as air and a lens, is based on the relationship between the refractive indices of the media. Snell's Law (Eq. 1) relates the indices of refraction n of the two media to the directions of propagation in terms of angles to the normal:n1 sin θ1=n2 sin θ2  (1)
The index of refraction (n) is defined as the speed of light in vacuum (c) divided by the speed of light in the medium (v), as represented by Eq. 2:n=c/v  (2)
The refractive index of a vacuum is 1.000. The refractive index of air is 1.000277. Representative materials used in microlens and semiconductor device fabrication include oxide, with a refractive index of 1.45, and nitride, with a refractive index of 2.0. FIG. 1 illustrates the relationship between the indices of refraction at the air-microlens interface. The graph on the right side of FIG. 1a shows a constant index of refraction in the air and a different constant index of refraction at all depths of the microlens, and therefore a sharp increase in the index of refraction at the air-microlens interface.
When light travels from a medium with a low refractive index, such as air, to a medium with a high refractive index (the incident medium), such as nitride, the angle of light with respect to the normal will increase. In addition, some light will be reflected. This will reduce the efficiency of the imaging system, since not all of the light hitting the lens will travel through the lens to the photodiode, for example.
Reflection at the interface of two different media can be quantified by the following formula (Eq. 3):R=(n1−n2)2/(n1+n2)2  (3)
Therefore, reflection from the interface between the two media can be reduced by matching their indices of refraction as closely as possible. As noted above, the refractive index of oxide is significantly closer to 1.0 than that of nitride. By providing an outer layer on a lens having an index of refraction closer to that of the surrounding medium, such as that of air, reflection is reduced and the efficiency and accuracy of the lens is improved.
Thus, it would be useful to have a microlens having a graded refractive index profile to reduce light reflection.